{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Variance Gamma Partial Integro-Differential Equation\n",
    "\n",
    "## Contents\n",
    "   - [The VG PIDE](#sec1)\n",
    "   - [Numerical solution of the PIDE](#sec2)\n",
    "   - [Comparison with Monte Carlo, closed formula and Fourier inversion](#sec3)\n",
    "   - [Comparison with the Black Scholes PDE](#sec4)  \n",
    "\n",
    "I suggest the reader to read the notebook **3.1** on the Merton PIDE, and the Appendix **A3** for an introduction to the Variance Gamma (VG) process.\n",
    "\n",
    "The knowledge of the VG process, is not necessary to understand this notebook, which is focused on the numerical solution of a PIDE.    \n",
    "In my opinion the [wiki](https://en.wikipedia.org/wiki/Variance_gamma_process) page is not that clear, and if the reader is interested to understand something more, I suggest to have a look at the notebooks **1.5** and **A3**.\n",
    "\n",
    "Now I'm going to present an approximated equation, whose solution converges to the solution of the original VG equation for $\\epsilon \\to 0$.    The reason for using an approximation, is that the Lévy measure is singular in the origin.\n",
    "Therefore, we have to remove the singularity from the integration region.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1'></a>\n",
    "## The VG PIDE   \n",
    "\n",
    "The approximated VG PIDE has the following form:    \n",
    "\n",
    "$$\n",
    "  \\frac{\\partial V(t,x)}{\\partial t} +\n",
    " \\bigl( r-\\frac{1}{2}\\sigma_{\\epsilon}^2 - w_{\\epsilon} \\bigr) \\frac{\\partial V(t,x)}{\\partial x} \n",
    " + \\frac{1}{2}\\sigma_{\\epsilon}^2 \\frac{\\partial^2 V(t,x)}{\\partial x^2}\n",
    " + \\int_{|z| \\geq \\epsilon} V(t,x+z) \\nu(dz) = (\\lambda_{\\epsilon} + r) V(t,x).\n",
    "$$\n",
    "\n",
    "with parameters   \n",
    "\n",
    "$$\n",
    "  \\sigma_{\\epsilon}^2 :=  \\int_{|z| < \\epsilon} z^2 \\nu(dz), \\quad \\quad w_{\\epsilon} := \\int_{|z| \\geq \\epsilon} (e^z-1) \\nu(dz), \\quad \\quad\n",
    " \\lambda_{\\epsilon} :=  \\int_{|z| \\geq \\epsilon} \\nu(dz) .\n",
    "$$\n",
    "\n",
    "and Lévy measure:   \n",
    "\n",
    "$$\n",
    " \\nu(dz) = \\frac{e^{\\frac{\\theta z}{\\sigma^2}}}{\\kappa|z|} \\exp \n",
    " \\left( - \\frac{\\sqrt{\\frac{2}{\\kappa} + \\frac{\\theta^2}{\\sigma^2}}}{\\sigma} |z|\\right) dz,\n",
    "$$\n",
    "\n",
    "where I used the parametrization coming from the Brownian subordination. See equation [35] in **A3** or [wiki subordinator](https://en.wikipedia.org/wiki/Subordinator_(mathematics)).    \n",
    "If you are reading quickly, and you have no time to study the Brownian subordination, just think of $\\theta$, $\\sigma$ and $\\kappa$ as the three parameters of the model.\n",
    "\n",
    "As I said before, the Lévy measure has a singularity at $z=0$.    \n",
    "\n",
    "The activity of the VG process is infinite, i.e. $\\lambda = \\int_{-\\infty}^{\\infty} \\nu(z) = \\infty$. Since the interval $-\\epsilon < z < \\epsilon$ is removed from the region of integration, all the parameters defined above are finite! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This equation is almost identical to the Merton PIDE, except for the truncation in the integral.\n",
    "\n",
    "At this point, we can restrict the computational domain on $[A_1,A_2]$ and the integral region on $[-B_1,B_2]$, following the idea presented in **3.1**.   \n",
    "\n",
    "Using the same discretization used for the Merton PIDE, we can solve the problem with the IMEX scheme.\n",
    "\n",
    "I will not re-write the discrete equation. Everything will be clear (hopefully) from the following python code:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2'></a>\n",
    "## Numerical solution of the PIDE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import sparse\n",
    "from scipy.sparse.linalg import splu\n",
    "\n",
    "import numpy as np\n",
    "import scipy as scp\n",
    "import scipy.stats as ss\n",
    "from IPython.display import display\n",
    "import sympy\n",
    "\n",
    "sympy.init_printing()\n",
    "from scipy import signal\n",
    "from scipy.integrate import quad\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def display_matrix(m):\n",
    "    display(sympy.Matrix(m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = 0.1  # risk free rate\n",
    "theta = -0.1\n",
    "sigma = 0.2\n",
    "kappa = 0.3  # VG parameters\n",
    "\n",
    "W = -np.log(1 - theta * kappa - kappa / 2 * sigma**2) / kappa  # martingale correction w\n",
    "\n",
    "dev_X = np.sqrt(sigma**2 + theta**2 * kappa)  # std dev VG process\n",
    "\n",
    "S0 = 100\n",
    "X0 = np.log(S0)  # stock, log-price\n",
    "K = 100\n",
    "Texpir = 1  # strike and maturity\n",
    "\n",
    "Nspace = 7  # space steps\n",
    "Ntime = 3  # time steps\n",
    "S_max = 3 * float(K)\n",
    "S_min = float(K) / 3\n",
    "x_max = np.log(S_max)  # A2\n",
    "x_min = np.log(S_min)  # A1\n",
    "\n",
    "dx = (x_max - x_min) / (Nspace - 1)\n",
    "extraP = int(np.floor(3 * dev_X / dx))  # extra points\n",
    "x = np.linspace(x_min - extraP * dx, x_max + extraP * dx, Nspace + 2 * extraP)  # space discretization\n",
    "T, dt = np.linspace(0, Texpir, Ntime, retstep=True)  # time discretization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In **A3** we defined the \"martingale correction\" term:\n",
    "\n",
    "$$\n",
    " w := \\int_{\\mathbb{R}} (e^z-1) \\nu(dz) = - \\frac{1}{\\kappa} \\log \\left( 1-\\theta \\kappa -\\frac{1}{2}\\bar\\sigma^2 \\kappa \\right).\n",
    "$$\n",
    "\n",
    "In the previous cell I defined $w$ (called `W`) just to compare it with $w_{\\epsilon}$.  We expect that $w_{\\epsilon} \\to w$ as \n",
    "$\\epsilon \\to 0$.\n",
    "\n",
    "Following Section 2.3 of **A.3**, I introduce the auxiliary parameters A and B.    \n",
    "They will make the Lévy measure definition more readable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = theta / (sigma**2)\n",
    "B = np.sqrt(theta**2 + 2 * sigma**2 / kappa) / sigma**2\n",
    "\n",
    "levy_m = lambda y: np.exp(A * y - B * np.abs(y)) / (kappa * np.abs(y))  # Levy measure VG"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The extra points are obtained by `extraP = int(np.floor(3*dev_X/dx))`, where `dev_X` is the standard deviation of the VG process. The choice of 3 stardard deviation is arbitrary, and in the pricer class this number is different (it is 5).\n",
    "\n",
    "The extra points are the points in the intervals $[A_1 - B_1, A_1]$ and $[A_2, A_2 + B_2]$.   \n",
    "In this case we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Under this discretization there are 1 extra points\n"
     ]
    }
   ],
   "source": [
    "print(\"Under this discretization there are {} extra points\".format(extraP))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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52ijF75phjgkEu9N9ttd/pHy8/efnNw5+4/BmXgQxg2J+1P2pldm1WDNYND/noJhPdfHwaxWR8zpGMGwJkoNifvYS6DqF2kguwa55xpzTf1i69o6iFEOeLZk96Wssa7PmiqwpQ/MiqoalrC0phlBsoHDvyhgmcAP3we7tknTY3F3/kWKhePxWborcycqPgR8FNfkubOC4KusaFJOtVuzsGJr35cF5n0cwh4I3fB/s7rfqnew/bR/ih39WhzmD4k5NAFdlvbpiChZvyV7L7h7A5QYUBz6zKyPMCIEbYmcvVo5mtRkMeJ5stt+lOBWfZ09+MmkemWQzs/5XV2+XkO5L+uloudMy5Nyr/o6ZFIjZMQ58ToDMcO6WnZSBWQpjz38oFgqEItnPHoRPMpA8p6oz0POiJ32Z09vErjBmVvJ4ScIDM5kP8orvLfcg+be3ceDzWxbhCgKrEpBCx4HPq7ZAZB4EJgis/ow5Ub4IDgI3SSAU8yabPSpdO4FQzNpbKMp3kwRCMW+y2aPStRNAMR+1hTS79jJH+YLAXgnEgc97bdmo16YJxIHPm26+KPzuCcQz5u6bOCq4RQKbVUztknhvCFx+7HN8OvSP+yCwNQLuvbJth7fv2djNz35DPjp9Nay0/Pj2DcNHznzvlj28WXLpIUhsUP5Cft6vSf4hWTa7W/64Mexn7IxkUFRXubtICzrm5C9ZF7e0eIrDAPWl7N55qalM6pYcnL5O/Ljv7Re1sDmyFufStsrkbk/Junh65cbqdm78XLquvbItjO9ld8f/tYX5qxLlq/Dukxm52ZV/dHhzK9ft4Nc9cqT5neyDbDrYP3Rx2nYjh/+YkcxvCkOZ6VjI800d+b6R3Ri5aURXudsoi1pz8pfsJLdc4RQPDnweZ1/j58Q6P8nBo6fEumfT9U+yYdiZObJdpAs6VB53e0rWxdMrN1atc+On6Sqt2XtlGXmGjckshBLYTvpDmzDLya6B5UaG+3R25KTqJwprlFLug9zMfC91pXIEjRk64590PdD1ri5m704p20iuco9lsIC/K3+VmwbxcOsVSfEYGN2mzYcOOzR8dZHOooc5ssPELni/KM+2jrO5W/3OjW/p5OyHOc+MH5/dcGjR40EYM2X6XMeobUvLVPSFbp4l8fn2MjcrEjeVS9MocXvLXZK2J443fy+3Lk+xZIXBQDQcjDqZjIPHim7VkwlPvebIpvEu6V6a52zug8qdG3+Q3Ntbr2KigBxgNNYJTGEB9/pt8p3LlDBVupzc722M3BfpXWIzHN5yz0hylqg3/0lumVw/V3uk3yRmRI68GCC9hx7PkT3K6EIeS/Ms4Z5W7dz4aVo9913vbuRGHYCRIWcYtQ8KZ1lpypmTMz+Wr290cc/z4dC803o8HQbk7pVOswRUGPGIwzNmN2PLPVnuXLpL+Xnyl4yLW1omxWEJ613yd1EVz33o8RzZLoMLO1SmyfaUjIunV26sSufGH0vX/L0zpsl3tgqGUqIM9sbTFO1NJ3TsMGg8c+aUr1F0hZnccQpvfZD5WeX4Thdl4OI/hDGKjZpMuUdlLxGQyX8Ot4Piw43BzVYhs4qpeHRum2l5ZoNXN5ilic2RTeNd060ylvbDWdwzdTo3fibJt17FiqkkeOnDCNy9wHmb7KjLZkReNhwUt1OiFrAp9WSnkzxvg03+IDdxWOpMzSQl5aa4S5mS/I0bZeCnEVOs2WVSXJ7v4cYzJLxQ9Oyhx3NklcZa5lyep8qdcj8lNxZWHP9O8BktH4ylnPNXHDo/z5zp0iL3zGjRbXRpniEVjxH/Lwrk901GPCrwor3GXgwpeNKgnDzHPtV1pNzyy5V7MtGlBEbyn8OteZ1eWh7lT3x+jrI37Axu8KZzcxYO5+I0g51st2xpec6NpzLm2tPL0ys3Vsxz4x+lq/ow4DaD7kPdvKeLU8EYOSeN5GgwnhV7b/d0b7PX40wi5tcpC/K6GP2bpahslrc2wnRymbQOkuUwptxrfxO3/OyeONlydwIXdozlL38XN8nRPo9ln2QzUQ2Wrvbo0YgqPbgze8KsW8HIPUdW4tc1Kne2PeXv5emSG6uVN5+x+Dl/6qTrv4Td5QTG/BSJ0ZXfDLuZUu5GoWXTYWxpNEzCZkzCTxlmz27UPiH4gcJyI1aTj8ryKo2r+6lyp+KLux35e7hR5w+VFrNbamDGCgF/VjE9xTNB+aN4KLZ1SAs6yI94KKjxc8t2iVzRobJOtaeHJyX2yo3V7tz4Y+n6FVMw6AB0jGHDA8meeegcjLRD8748eHPbdIoWLJsM/pL40RkYsZGdMj9kykEc4gOrM5LzlLuTX9rhzN/DjXr16kZZlf4f+MvuBkv8h0bhrFC4sst8ycO/SX+O7DCfS9+rbJ729PCkqF65sWqdG38s3cOcLXm/KpWjjiE/nulYCjVGbraIsQuHEfggmwb/t66P5G5mMtm87uc5h+cdU1bSZ8+mKflBbuLS8VDqTmHlZpYmD3tWOshNml/rSpUdOVe5Jbe4acvpyl+yk9xyBVQ8lj4oZvdoIfcYNwYuBk7aouFOmnKzLGQ27V7kye2WJY1rGJXJ3Z6SdfH0yEkmy5M6e+J72Sgt2oEtkw/unJHoXEAh4tD0lo0KRIFOHt6sjHmufEdyX8um0hji9BRf94zwLJFfNhLtH/x0Ic/DP4YlGEvbTinxlJlT7vsYy/6dk/8kt7Robd1pEwyDI6P3C9mwHeOGAvNG/OShxyQoObcs8lcyl+A5yX2MZ1vnyfglbFwzZknCEScIBIF5BDQAdDPmw3lRQzoIBIFrEAjFvAblyCMIzCQQijkTWIgHgWsQCMW8BuXIIwjMJBCKORNYiAeBaxAIxbwG5cgjCMwkEIo5E1iIB4FrEAjFvAblyCMIzCQQijkTWIgHgWsQCMW8BuWF8tDOEDag82mQbWOcnbLisgm8Z0hP19Oep27myA7j3uo9HHWd1Uaw8+6VpZFoONs0Tsfg/mh/q/x6RvHoCHx3aXGb8DY9+1KFT5rY68rG9OHe20Z+7E+bPvtEuw3xQ1nJ2J5agthX+4X83gzlLnGvfFzcnHKwpC5sdM4Vlz2yf8oFJH6ug7Jb+TmySRbLOJ1MDjPlluhzwy+oflIZrN8u0UY+xVSmKOLwaw4+9+KD5U91NV+SjDQHSmOFbkQkT2elc6VfRFBZzuzhq/reZvYmUvJH4ZTnR10oM0pNekemleODavJKD5b+t+5dB0sfJTrDo81/kptXTll/qAs2uY+l+RrEOp2cowZmGDoQ6dB2HGKWG6jmyCqZ5YyXyQy5s/ocNVNepEF/pk2bPiqbey77wmqJNvIppjJlcy3TM4poSmjKw6dW5ifnWyPZsQOJUcLhDEplyYdKnhz1JUcnar4/bPOgk+UMynt0sLTivJQ/M083MOQiL+Dn5eaVO6jsR2WWXzMwyc62w6AefEJ38tvNRH6ObBJtEaeXiVfurD7X1oi+yexofR9vJoneQKnwc9vo8JCUHYYZD2XoRlVl3rlz8RWOsvTiJHKM7p4DpJMoRU5m9R60NhXq80xlfFyUqj+Sl5tX7sVI1jxS9Aa6EbkteXuZeOXO6nPiS1+iT3ffCwNT/qzwUkVcpI3uSHzKKGNGiN4sJj8Kikmf3+597v9+LpneMi4JJD3OGhpT7rMVRmlbGq+TfM2ZHiydjn4WvoitMri4zZA7mhEVl5ngb4sUuKJEZjBxMVbVzu1zDHw8w4/12YaewhdpI5diDttLmTP6NEsDuXsjCLLyO3kgscLHllLNklThjIJnGaUBRNJ4kkmIj7QxzRLw3nn5vyrPSW5WghlylJ8BzvNsackfJM/yj4ELDqTBM2aW+RxZpXMxo3KcxU7xz+1zvMvgA3366Oe6GNx5rsz+pzT5N0byRW10Zwl47LZQAPpQFw3Js1rPtAVBKXJLyJ5setOmTSVmdbI0jYyb0YvyDk0zAMjTZtVh+KL3Hm5k6JVLCsfgyDXHUOeflVcz8suGOY8VuZduc2TnlMEt62XilUszbuN4+5z1lQ8Ur+ujcv+hi7f8RzNlm1dJG7mfMZs8lDkvAzi6gtHnJ128RbUlbVuO4gOJebCee4C05Tlmf0GAytgpp9woZdMpZc8aPEirxChPDzfK6ZKjDJKlQz2TPWspLnkU0Op/kBsGpHH0SDJHVvEvYlQGFxOv3KCQrj6ntE0pWZ0MV4g/K02OajGZLgv5FbURCTzsUpnpUKaMEDQwU3lTKNkskY4aeCppxSMOy4Sx5cZUEtlwpUf5OFian3T+qovRC1j2gH4VxVR+nVEZjrh1gYnDIcczz1LlJx1+GIfNlJkjO5XWrHAHkyY9j5xkSvpcjjc/x9H/WeoOTXEbuZayqkSz9JM9fA55qZIwGzFyE/ZYdq7wwwJ395JHmflJI32z1YWf61C6KCeAOiM/W/7NKmuXgNOhfCa5KSlWCS65QbasVGaVX/lwmBWsOUAqZ5oBloA5srmEzvVT/i4mXrm0PIozq89J3t5X0JfGTG5Qm91GlvhDc0zYjAosW7uGy8hTsOZAYskxizaX/ACM4nJvCtFE1z0FPzpAWv65SjZxFvpDmTgF7hToJbLycCMfr1xTJpWbdoDR3PIzqufa8AkJK9104J0jS/SljZeJV64pn+pY2udY7ufYWb17g+QZbdSk55oxJUkHyHVkGg9jYUfPOypg9kBi+aMcUwdIN4mX/mkbgU0G3bGWLTBm+bFZozS7XLxJbm0kr5zlYdxfm4fTdh+UrfTmyDqznyXmZeKVO5zZ51j68kw6NPQjZtRh3y9toyZ9r2J2b6GsVCoII89jXeyDBc6YQYarM5JntKeSKPTwmZTZ1bbPEe/owOcuoXsHr/wxjPrDcpDPsPOSL2VOZwd5XcR4uXnlrJDGc1jfJlx1G+PG1kSubmkvt+3OGj7fz5G1ci1pe5m45FTPs/qc4vPIQX9lM0eTp2w4f6areck4qPzJNhrIHt26z5VVIZhl0sajohRyOFI0mcgfhUOGeBheeryQP291OSWbsJzhLVw3m7WyAOk6E5F0b6MX6QMBRWM5wbbB7s2Z3LZ8NlAsqbNlVtzFjfJycfPKUUDJwo4l3OhresnAOMeNuNaZGcwYuNgI8kZ2z7T5uGR7ERe6Uf6LsWt5nNXnqJbSoT9ZX4Jf9jdgyU22EemlRnGal6eyH7gVM00g3EEgCCxPIFXMh8snHykGgSBwLoFQzHMJRvwgcAECoZgXgBpJBoFzCYRinksw4geBCxAIxbwA1EgyCJxL4C5JgC8MktvGyW836U8kw/C4DwJBoICA9OrUT4YHFJPf/nq/ESb59LYZJf7hDAJB4DwC9vt6NpX/B/GaMu0UFjzLAAAAAElFTkSuQmCC",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 44.22\\\\0 & 0 & 108.01\\\\209.52 & 204.88 & 200.0\\\\342.19 & 337.55 & 332.67\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  0       0       0   ⎤\n",
       "⎢                      ⎥\n",
       "⎢  0       0       0   ⎥\n",
       "⎢                      ⎥\n",
       "⎢  0       0       0   ⎥\n",
       "⎢                      ⎥\n",
       "⎢  0       0       0   ⎥\n",
       "⎢                      ⎥\n",
       "⎢  0       0       0   ⎥\n",
       "⎢                      ⎥\n",
       "⎢  0       0     44.22 ⎥\n",
       "⎢                      ⎥\n",
       "⎢  0       0     108.01⎥\n",
       "⎢                      ⎥\n",
       "⎢209.52  204.88  200.0 ⎥\n",
       "⎢                      ⎥\n",
       "⎣342.19  337.55  332.67⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Payoff = np.maximum(np.exp(x) - K, 0)  # Call payoff\n",
    "V = np.zeros((Nspace + 2 * extraP, Ntime))  # grid initialization\n",
    "offset = np.zeros(Nspace - 2)  # vector to be used for the boundary terms\n",
    "\n",
    "V[:, -1] = Payoff  # terminal conditions\n",
    "V[-extraP - 1 :, :] = np.exp(x[-extraP - 1 :]).reshape(extraP + 1, 1) * np.ones((extraP + 1, Ntime)) - K * np.exp(\n",
    "    -r * T[::-1]\n",
    ") * np.ones(\n",
    "    (extraP + 1, Ntime)\n",
    ")  # boundary condition\n",
    "V[: extraP + 1, :] = 0\n",
    "\n",
    "display_matrix(V.round(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us define the cutoff term $\\epsilon$ and the relevant parameters.\n",
    "\n",
    "Note:  The integrals are performed using the function `quad`. The integrals are split in the two regions: \n",
    "$[-B_1, -\\epsilon]$ and $[\\epsilon, B_2]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps = 1.5 * dx  # the cutoff near 0\n",
    "\n",
    "lam = (\n",
    "    quad(levy_m, -(extraP + 1.5) * dx, -eps)[0] + quad(levy_m, eps, (extraP + 1.5) * dx)[0]\n",
    ")  # approximated intensity lambda\n",
    "\n",
    "int_w = lambda y: (np.exp(y) - 1) * levy_m(y)  # integrand of w_eps\n",
    "int_s = lambda y: np.abs(y) * np.exp(A * y - B * np.abs(y)) / kappa  # integrand of sigma_eps\n",
    "# avoid division by zero\n",
    "\n",
    "w = quad(int_w, -(extraP + 1.5) * dx, -eps)[0] + quad(int_w, eps, (extraP + 1.5) * dx)[0]  #   w_eps\n",
    "\n",
    "sig2 = quad(int_s, -eps, eps)[0]  # the small jumps variance\n",
    "sigJ = quad(int_s, -(extraP + 1.5) * dx, -eps)[0] + quad(int_s, eps, (extraP + 1.5) * dx)[0]  # big jumps variance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we computed $\\sigma_{\\epsilon}^2 :=  \\int_{|z| < \\epsilon} z^2 \\nu(dz)$ we can compute also $\\sigma_J^2 = \\int_{|z| \\geq \\epsilon} z^2 \\nu(dz) $.    \n",
    "We expect that $\\sigma_{\\epsilon}^2 + \\sigma_J^2 = \\text{dev\\_X}^2$.    \n",
    "Due to the limitation of the integral in $[-B_1,B_2]$, the two are not perfectly equal. But for a big enough choice of $B_1$, $B_2$, the equality is satisfied, as we can see in the output of the cell below.\n",
    "\n",
    "Let us inspect better the parameters we obtained:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eps =  0.5493061443340548\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The intensity lam=0.001472 is very small because the mass is concentrated inside [-eps,eps].\n",
      "\n",
      "Theoretical w:  -0.07905508872438688\n",
      "Approximated w, w_eps =  -0.0005999810394699548\n",
      "Integral of int_w inside the truncation [-eps,eps]:  -0.07844382431861505\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The VG variance 0.042981 is equal to the sum of the Var of the decomposed processes 0.043000.\n",
      "Under this discretization the diffusion variance 0.042396 is the major component. \n"
     ]
    }
   ],
   "source": [
    "print(\"eps = \", eps)\n",
    "plt.plot(np.linspace(-1, 1, 100), levy_m(np.linspace(-1, 1, 100)))\n",
    "plt.title(\"Lévy measure\")\n",
    "plt.show()\n",
    "print(\n",
    "    \"The intensity lam={:.6f} \\\n",
    "is very small because the mass is concentrated inside [-eps,eps].\".format(\n",
    "        lam\n",
    "    )\n",
    ")\n",
    "print(\"\")\n",
    "\n",
    "print(\"Theoretical w: \", W)\n",
    "print(\"Approximated w, w_eps = \", w)\n",
    "print(\"Integral of int_w inside the truncation [-eps,eps]: \", quad(int_w, -eps, 1e-10)[0] + quad(int_w, 1e-10, eps)[0])\n",
    "plt.plot(np.linspace(-1, 1, 100), int_w(np.linspace(-1, 1, 100)))\n",
    "plt.title(\"(e^z-1) * nu(z)\")\n",
    "plt.show()\n",
    "\n",
    "print(\n",
    "    \"The VG variance {0:.6f} is equal to the sum of the Var of the decomposed \\\n",
    "processes {1:.6f}.\".format(\n",
    "        sigJ + sig2, dev_X**2\n",
    "    )\n",
    ")\n",
    "print(\"Under this discretization the diffusion variance {:.6f} is the major component. \".format(sig2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parameter $w_{\\epsilon}$ (i.e. w) is very different from the theoretical $w$ (i.e. W). This is a consequence of the discretization.    \n",
    "I showed that the integral of $(e^z-1)\\nu(dz)$ on $|z|>\\epsilon$ is almost zero.     \n",
    "It follows that the integral in the region $|z|<\\epsilon$ is almost equal to $w$.\n",
    "\n",
    "Ok... now that we have some confidence on this topic, we can continue with the solution of the PIDE.     \n",
    "As usual we create the diffusion matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "dxx = dx * dx\n",
    "a = (dt / 2) * ((r - w - 0.5 * sig2) / dx - sig2 / dxx)\n",
    "b = 1 + dt * (sig2 / dxx + r + lam)\n",
    "c = -(dt / 2) * ((r - w - 0.5 * sig2) / dx + sig2 / dxx)\n",
    "D = sparse.diags([a, b, c], [-1, 0, 1], shape=(Nspace - 2, Nspace - 2)).tocsc()\n",
    "DD = splu(D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following cell, I create the Lévy measure vector. \n",
    "\n",
    "The three points in the middle are zero!     \n",
    "This is because the Lévy measure is truncated near the origin, and the region $[-\\epsilon, \\epsilon] = [-1.5\\Delta x, 1.5\\Delta x]$ is excluded."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.00140784532775271\\\\0\\\\0\\\\0\\\\6.46388528653557 \\cdot 10^{-5}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0.00140784532775271⎤\n",
       "⎢                   ⎥\n",
       "⎢         0         ⎥\n",
       "⎢                   ⎥\n",
       "⎢         0         ⎥\n",
       "⎢                   ⎥\n",
       "⎢         0         ⎥\n",
       "⎢                   ⎥\n",
       "⎣6.46388528653557e-5⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nu = np.zeros(2 * extraP + 3)  # Lévy measure vector\n",
    "x_med = extraP + 1  # middle point in nu vector\n",
    "x_nu = np.linspace(-(extraP + 1 + 0.5) * dx, (extraP + 1 + 0.5) * dx, 2 * (extraP + 2))  # integration domain\n",
    "\n",
    "for i in range(len(nu)):\n",
    "    if (i == x_med) or (i == x_med - 1) or (i == x_med + 1):\n",
    "        continue\n",
    "    nu[i] = quad(levy_m, x_nu[i], x_nu[i + 1])[0]\n",
    "\n",
    "display_matrix(nu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code is the same we used for the Merton PIDE. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Backward iteration\n",
    "for i in range(Ntime - 2, -1, -1):\n",
    "    offset[0] = a * V[extraP, i]\n",
    "    offset[-1] = c * V[-1 - extraP, i]\n",
    "    V_jump = V[extraP + 1 : -extraP - 1, i + 1] + dt * signal.convolve(\n",
    "        V[:, i + 1], nu[::-1], mode=\"valid\", method=\"auto\"\n",
    "    )\n",
    "    V[extraP + 1 : -extraP - 1, i] = DD.solve(V_jump - offset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.467523461720827\n"
     ]
    }
   ],
   "source": [
    "# finds the option at S0\n",
    "oPrice = np.interp(X0, x, V[:, 0])\n",
    "print(oPrice)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### All good!!\n",
    "\n",
    "**Alternatively** we could have used the Jump matrix. \n",
    "Let us do it for completeness, but remember that the `signal.convolve` method is more efficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.00140784532775271 & 0 & 0 & 0 & 6.46388528653557 \\cdot 10^{-5} & 0 & 0 & 0 & 0\\\\0 & 0.00140784532775271 & 0 & 0 & 0 & 6.46388528653557 \\cdot 10^{-5} & 0 & 0 & 0\\\\0 & 0 & 0.00140784532775271 & 0 & 0 & 0 & 6.46388528653557 \\cdot 10^{-5} & 0 & 0\\\\0 & 0 & 0 & 0.00140784532775271 & 0 & 0 & 0 & 6.46388528653557 \\cdot 10^{-5} & 0\\\\0 & 0 & 0 & 0 & 0.00140784532775271 & 0 & 0 & 0 & 6.46388528653557 \\cdot 10^{-5}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0.00140784532775271           0                    0                    0    \n",
       "⎢                                                                             \n",
       "⎢         0           0.00140784532775271           0                    0    \n",
       "⎢                                                                             \n",
       "⎢         0                    0           0.00140784532775271           0    \n",
       "⎢                                                                             \n",
       "⎢         0                    0                    0           0.001407845327\n",
       "⎢                                                                             \n",
       "⎣         0                    0                    0                    0    \n",
       "\n",
       "       6.46388528653557e-5           0                    0                   \n",
       "                                                                              \n",
       "                0           6.46388528653557e-5           0                   \n",
       "                                                                              \n",
       "                0                    0           6.46388528653557e-5          \n",
       "                                                                              \n",
       "75271           0                    0                    0           6.463885\n",
       "                                                                              \n",
       "       0.00140784532775271           0                    0                   \n",
       "\n",
       " 0                    0         ⎤\n",
       "                                ⎥\n",
       " 0                    0         ⎥\n",
       "                                ⎥\n",
       " 0                    0         ⎥\n",
       "                                ⎥\n",
       "28653557e-5           0         ⎥\n",
       "                                ⎥\n",
       " 0           6.46388528653557e-5⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "J = np.zeros((Nspace - 2, Nspace + 2 * extraP))\n",
    "\n",
    "for i in range(Nspace - 2):\n",
    "    J[i, i : (len(nu) + i)] = nu\n",
    "\n",
    "display_matrix(J)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Backward iteration\n",
    "for i in range(Ntime - 2, -1, -1):\n",
    "    offset[0] = a * V[extraP, i]\n",
    "    offset[-1] = c * V[-1 - extraP, i]\n",
    "    V_jump = V[extraP + 1 : -extraP - 1, i + 1] + dt * (J @ V[:, i + 1])\n",
    "    V[extraP + 1 : -extraP - 1, i] = DD.solve(V_jump - offset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.467523461720827\n"
     ]
    }
   ],
   "source": [
    "# finds the ATM option at S0\n",
    "oPrice = np.interp(X0, x, V[:, 0])\n",
    "print(oPrice)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3'></a>\n",
    "## Comparison with Monte Carlo, closed formula and Fourier inversion\n",
    "\n",
    "\n",
    "Let us compare the ATM prices obtained from different numerical methods. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from FMNM.Parameters import Option_param\n",
    "from FMNM.Processes import Diffusion_process, VG_process\n",
    "from FMNM.BS_pricer import BS_pricer\n",
    "from FMNM.VG_pricer import VG_pricer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creates the object with the parameters of the option\n",
    "opt_param = Option_param(S0=100, K=100, T=1, exercise=\"European\", payoff=\"call\")\n",
    "# Creates the object with the parameters of the process\n",
    "VG_param = VG_process(r=0.1, sigma=0.2, theta=-0.1, kappa=0.3)\n",
    "# Creates the VG pricer\n",
    "VG = VG_pricer(opt_param, VG_param)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PIDE price:  (it takes about 5 minutes to run)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left( 13.3929725106497, \\  59.3151340484619\\right)$"
      ],
      "text/plain": [
       "(13.3929725106497, 59.315134048461914)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VG.PIDE_price((30000, 30000), Time=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "VG.plot([50, 200, 0, 100])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Closed formula**:\n",
    "\n",
    "The semi-closed formula is a complicated expression presented in [1]. I will not describe it here.    \n",
    "However, it doesn't work properly. It has a negative bias. Read comments below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 13.2040165334996$"
      ],
      "text/plain": [
       "13.204016533499598"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VG.closed_formula()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Fourier inversion**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 13.4046822776835$"
      ],
      "text/plain": [
       "13.404682277683463"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VG.Fourier_inversion()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Monte Carlo**:\n",
    "\n",
    "(the output includes the price, the standard error and the execution time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([13.40509225]), array([0.0034819]), 2.081190824508667)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VG.MC(20000000, Err=True, Time=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `MC` uses the following code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Monte Carlo, call: 13.404656210687538, put: 3.8857717094334183\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/_p/fvph973x59g67y9qng1ltjgr0000gn/T/ipykernel_69845/2615911637.py:9: DeprecationWarning: scipy.mean is deprecated and will be removed in SciPy 2.0.0, use numpy.mean instead\n",
      "  call = np.exp(-r * T) * scp.mean(np.maximum(S_T - K, 0))\n",
      "/var/folders/_p/fvph973x59g67y9qng1ltjgr0000gn/T/ipykernel_69845/2615911637.py:10: DeprecationWarning: scipy.mean is deprecated and will be removed in SciPy 2.0.0, use numpy.mean instead\n",
      "  put = np.exp(-r * T) * scp.mean(np.maximum(K - S_T, 0))\n"
     ]
    }
   ],
   "source": [
    "N = 10000000\n",
    "rho = 1 / kappa\n",
    "T = 1\n",
    "w = -np.log(1 - theta * kappa - kappa / 2 * sigma**2) / kappa  # martingale correction\n",
    "G = ss.gamma(rho * T).rvs(N) / rho  # gamma random vector\n",
    "Norm = ss.norm.rvs(0, 1, N)  # standard normal vector\n",
    "VG_RV = theta * G + sigma * np.sqrt(G) * Norm  # VG vector obtained by subordination\n",
    "S_T = S0 * np.exp((r - w) * T + VG_RV)  # exponential dynamics\n",
    "call = np.exp(-r * T) * scp.mean(np.maximum(S_T - K, 0))\n",
    "put = np.exp(-r * T) * scp.mean(np.maximum(K - S_T, 0))\n",
    "print(\"Monte Carlo, call: {}, put: {}\".format(call, put))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Put option"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt_param_p = Option_param(S0=100, K=100, T=1, exercise=\"European\", payoff=\"put\")\n",
    "VG_p = VG_pricer(opt_param_p, VG_param)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PIDE price:  3.8869336517616953\n",
      "Fourier price:  3.8884240812794104\n",
      "Closed formula price:  3.687758337095545\n",
      "MC price:  [3.89222802]\n"
     ]
    }
   ],
   "source": [
    "print(\"PIDE price: \", VG_p.PIDE_price((12000, 9000)))\n",
    "print(\"Fourier price: \", VG_p.Fourier_inversion())\n",
    "# the closed formula for the put is calculated by PUT/CALL parity\n",
    "print(\"Closed formula price: \", VG_p.closed_formula())\n",
    "print(\"MC price: \", VG_p.MC(10000000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "VG_p.plot([50, 150, 0, 60])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Remark:\n",
    "\n",
    "There are some discrepancies between the outputs of the four numerical methods.    \n",
    "\n",
    "- The Monte Carlo and Fourier prices are the most reliable\n",
    "\n",
    "- The convergence of the PIDE, when considering the Brownian approximation, is quite slow.\n",
    "  - For the put option we didn't need a huge grid in order to obtain the right price.\n",
    "  - But for the call option I had to use a huge grid (30000x30000). I expect to achieve a better convergence level for higher grid resolution, in particular when increasing the number of time steps.\n",
    "  - Increasing the computational domain $[A_1,A_2]$ may also help.\n",
    "\n",
    "- The semi-closed formula used in VG_pricer is taken from [1]. In my opinion, this formula is not very accurate.     \n",
    "  Unfortunately, I was not able to implement the closed formula proposed in the same paper [1], which relies on the     Bessel function of second kind (well...I tried, but it doesn't work. In VG_pricer it is called `closed_formula_wrong`).     \n",
    "  Therefore I decided to use the semi-closed formula, which is based on numerical integration. \n",
    "  However, this formula still does not produce very accurate values. \n",
    "\n",
    "If you have any comment on these features, please let me know."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec4'></a>\n",
    "## Comparison with the Black Scholes PDE\n",
    "\n",
    "Now let us compare the VG curve with the Black Scholes curve, for a European call option.    \n",
    "The volatility of the BS model is chosen equal to the standard deviation of the VG process. \n",
    "\n",
    "In this case I'm going to select some parameters with the purpose to have high values of skewness and kurtosis for the VG distribution.    \n",
    "In the VG process, the parameter $\\theta$ is associated to the skewness, and the parameter $\\kappa$ is associated to the kurtosis.\n",
    "\n",
    "Looking at the plot we can notice the different shape of the two curves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard deviation:  0.37416573867739417\n",
      "skewness:  -3.05441419328485\n",
      "kurtosis:  14.387755102040819\n",
      "Changing the sign of theta, the skewness becomes:  3.05441419328485\n"
     ]
    }
   ],
   "source": [
    "# Creates the object with the parameters of the option\n",
    "opt_param = Option_param(S0=100, K=100, T=1, exercise=\"European\", payoff=\"call\")\n",
    "\n",
    "# Creates the object with the parameters of the process\n",
    "VG_param2 = VG_process(r=0.1, sigma=0.2, theta=-0.2, kappa=2.5)\n",
    "VG_param3 = VG_process(r=0.1, sigma=0.2, theta=+0.2, kappa=2.5)\n",
    "diff_param = Diffusion_process(r=0.1, sig=np.sqrt(VG_param2.var))\n",
    "\n",
    "print(\"standard deviation: \", np.sqrt(VG_param2.var))\n",
    "print(\"skewness: \", VG_param2.skew)\n",
    "print(\"kurtosis: \", VG_param2.kurt)\n",
    "print(\"Changing the sign of theta, the skewness becomes: \", VG_param3.skew)\n",
    "\n",
    "# Creates the object of the pricer\n",
    "BS = BS_pricer(opt_param, diff_param)\n",
    "VG2 = VG_pricer(opt_param, VG_param2)\n",
    "VG3 = VG_pricer(opt_param, VG_param3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWgAAAAVCAYAAABrLnR+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAMNklEQVR4Ae2d7ZEVtxKGhy0CWO+NwCYDYDPAGWAcAZCBXf4F/yg7A9sR2DgD+0YAJgNzIwBvBtz30apFzxxp1DrMFgs1XTVHX63+UqvVo3MWbrx7927y8PTp06/0vPZ9e323wG6B3QK7Ba7WArXYe+JZCuE7tW/7vk+xnhV9pPL0U5T/Osk8akvhH/gP6wCd66TXqCwfS6+PxXfUPh8LH7/S87nsdXQhBhe4YRm0Bu6r91zl92XUVdTPxnuu547qF26oVNX/c2lM05nqD1u4Di9VhccGfpz7Cay0f1T/X7kvFWoz9oPro/3c46mOLsjaggvhfGGDqod4O/wfrZ7L30TjlfVlembHu+p/q+d7j7PA3URvo2ml+PXkvApb/iv+0DV7UAcO/EbyHe0vlyTHPp093mjmLT34V+htUXghvYS3tS+N8A35HFaTnOYbq7bYGg/eHkSfuPJYpe2BNKw2duzqI7zwXo/S9PJR17yqjB5POGZP657FBOvMtJpxVOMEaOLTL8y5yYcaaaOqvEPbIPf/qjYBhkCD0Q4g4/2tgZ9V/wkElSj1P5VszNVNoHH4E8DKIqmO4f9U+Y2eP1Q3YFMVPDrVJkCTpRneuboJ7DW+99RvC8/cMG/hoj/GRdZ0cKikzcOGnzIOdviaNqA6i/c3fXrKgaN6mLfmR/SG3SS6XTkTYoxm2JaZJr4CsP7YnzV5JpkuVCbIeh/tL0ZnpBRP+CFH8hGTQSVrUvOTJfmoXiE/Fs/oGkX4Qivkcygl3iFbbI23NGhus3de+bFsm6g+If8cpOnFoX4goyFkuoyvxQT2eTeOQlP0ftJDrPhdz0UK0OongPhsBtwJBBXf5Pra9QfMz4SfgnPGf6X2S9WhW4IVYxV4pD5eUwjIFmQtkJEt26YCD+dawkN1/FePzZ1E54Cn+nBkxgqemiHezBOwEJyMJht9GN9vcGy5PEBYPPgwv2Tuqod457khvUUT6Mo5QlO4UVvCm3VPPkOjAR/qLw2y9e6sqz/AJ/WRpeAHEf+EcESv0HpmKbtrlPEifMM+F7XF1nhZl1khHrPXeTcY1oc5ohPxzyGaJsuKjIbSXUfRiMZRo4lPJnlPcs8DEUkptWEMlmS7PkjZdE7Ge6JNEFsD8FCCJ0FWyppWkqUeLIYNuvKFq/vqQRaqwRBvyYOOZIUzO6mfDMzLRIb+j/qWOhPUCRLpkFAdCPEWXlTvSfSjckZpjtgyKRX4+FB/CbCYoXBgYOsloFvEP5fzWu3Qeg6sUYvPsn/E56K22BpvJrNswF6a7XmHMKJP1D9HaCZROjJOV7COxpcYQ0w+vZmZ1IKrs1e7CpE8+raC9Sb33VXps84Zqmgw5jPLKcsFHqeJAYvxncb+VMnVBwsMcNoUPPX7DDkhqA+cZ6nhPtQf5U1WTNZlPB2VWRV6t1fwzF7TAO+Q3lmKqJwhmpIxbMuZFRoN0TP9j/aXBum1bjbn7GDNyOb3jB/ouUawNjawntE1qrGp9YV9TpOjttgabyn3t7LX7DrIIYT1GfDPME0nx5qMoG29jo51Sngf3FQP2R/CHwUyEEGLuWcVAv/JfT5rrKDNu0QP50gpvuplY6n+B4/GyMD+VZ27ZDJBfzWi5hyEB3+CZrl7nmO8bwmnylsYHDKvNc7J/60eDh94L7+gbL3eM2/S/FomxxBjVd7qH9E7KucIzSRflrFrS8nLqz6BmPUHn7vfpLfKzf1F9JsgfnYgNHE0UPPdA/w1vQ6Q1SH86npqKLRGRrPHV+MhnxNeyBZb45keVoo+VxslobJ+K6P6GL4vNbfqn6M0ezJmnkPr6OUM1InJX9/UB0yaxgoQAoWgiTMuIQUldUYcY5JRwIfOuR429Es9M8DQepCXIEAQJwuiXAPGV3ECvE2Hu8ItgV51Dgp+rdLMwDSGXjhOmeeFzeNb6R2WU3yvwpbwT19woKN4oDdXPv4L0k38BfoBsOB7sYJrNltBST7c0yvNl649PzZ+EV+K2PNA7izD0ueittgar8iX/YFD2t5eythapaFPbUp3r9ukFs0BGUfW0dhGy3+EeO9EHzCpvW5GCYH3kA8pVoJ0Vv6CfkFoMTSHL0T4FpOM4Dc9fJt5HwIGuQ1dsldOGQsAMzyHz/g9zVt9S9B4k7fGbCHIwktGn3n8rvJXh2OsfflcDTLW8iWqH1R/k7fhCQf9VvV2MoTkjNA0/pTC79pSOARiW3fmsPbY3icBm/gLMm0E9qbXJBfUK80XbnM9NTbkSyN8F8Kv+twC1ze7tsjIx+Lxk7rlHvL8W/WuPqLb9c8F8RbNroyj67jgG2kSk7860QenZdlQkZlLHAnL/C/1kJFxR8wphrFe6AFCAfoS9fJTNMiyoJt+Qkev+siaCQDcXXHdwPWMvd61giT3REP8RfeAt2gANTr8uoJNx5vIAYgWgQlZTc4DHN9R462+Ub27ch5BEzGHbZl1Qx5+hI9PTCo395fMp1asJR+WKdp3JbX5a30zvWqI0nUzX3L0V/mKZ8vnorbYGi+JLrnwY39QO5Xa1RV9lpPC/tmieYSM3b22FDLYhu4pAXoTkGK8tnDykAETQHFMO2VrShS+wiXju1063lde5qpl5gT+2TVB5kM2TZA0vDwtFWSeTYeL8BYOAQWw8rI1/0zBx3dpHg55ppKD5AAivPOkkN6DcoZoLoTu2ZLvAjiwWsAaJUBWPUf5i9GIlM4mhbebZ309/wzpJV5dP3bydH1JuCG+Tp9Jc5o+53ib3n6q9ZFMmGzW90F4TBZN9sepylVbe0Z5XlOfJa7aq/5p+JKhSnNERuGajaw08r48iAl+sFNPifNNIRG8agvRmR8aJuj+5ZRpTUqbWnhftHDVj4ws8IFB1IdTcSBYRpT45DkY6VXqqH90eedpdp1Sp7LIrsUbZ7mlsmTOqqcFU2lO2uUt3FG9u3IeQXPKc3q2vCuda4dhWhfRWFsH7Br1F3BHoGUT8xfG1yCqV3c9M5OWPCaD+UeUb5on+0Z8rsV7aYut8fCdc8nItYIH1py3K/rZxyUBC+qTaAmXfdLzz2mNZp4/ImPLRkkmfdg6WnukRJ+3BGiIpMAxMtvjZqX544MvVU8BVCUMyGjveNxGnTm1QI6DAmkM2npYzJri8MNgHmx+LWgYXpd3RuTVbOlcDKEfchXequN0LHRxNhAFbCB//9blLRrQHtE7JOcgTWSP2PKXis7MxQ+8fbBD2F9E8xR5IXQksG68MSyBteO+uEc7pJdoddczCxBaI+FG+U7SIepzUVtsiif5WP/iA9kOyM2fsrO/SyLDmNpRfYxU1z97NDVOXAnLKNzoOpqMI+WZkF+f6IOs5jww064rmLgEAvwyCLLAvMKWrEl1Nto7PSnTcEQIZPy2uYBw2MSneqBhG4hFLHfShqxxXll4HVwGbuYDNv+yNf8M8RZtMnQcqWx01aH/QE/60guy6sMW6I6u/LlqedTndVEzXddsqrf4heQU76uwZdIVxQwkj/21mN+AIX+BhuZjY34ps/QZY9EtNZdD8a1KfCpBprtcu5Z/RvXa1JckaIivdAn73IAtojYL4WWz1wrWl6fAiD5l0nsaF66vVI+kafMPZGRANKN7zehQrsVRj5eShxtPnjzhpCLocY97AOon2ABkQQhKwCUQEhBLNqi6BS4z9uz3wcJPIDx+PkKg40K/gNrQX25i/vJvdqKpjbw/6PEHQosXjsvG7v0MLsRbdCbxR0/TkcPqmfr8IYR+8K0B2RqGL6B2iLfwwnpDXPircmacME3Ri9oSPHtzwD6sE99JXMDTIMtH02xZXUMQhItNgYN/cOmyu/8pGvDBJsjxRs+5ntnaqW28av4Z1Su0nplXZI26fLN9wKtBzeeittgUzwsnmck+kRl7AQS7F+rnO6yhPcRkzYFWc68fSbMpIzwNRDuyjqE46mhig8fpX7PLwvMLjBJoDHEvdwtcBwvIN8l+CZwE2B12C3y2FpCPc9iQAN86yVpyAswy2s9W+12xT9UC3OnvwflTXb1d7hEL8AZKTJ5SgJbjc1VRfqfKwA67Ba6LBeSfvGpzLbHDboHP2gLydbJnYnG6PrYMGqW5/+XOZYfdAtfNAo/ksNW/wrxugu7y7Bb4QAsQg8ttRvkfVSCao/f9fTN8oIn36bsFdgvsFhi0gOIuv3jin4Qov0b7P8xE858jFevFAAAAAElFTkSuQmCC",
      "text/latex": [
       "$\\displaystyle \\left( 19.3873623868759, \\  0.536520004272461\\right)$"
      ],
      "text/plain": [
       "(19.38736238687595, 0.5365200042724609)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BS.PDE_price((7000, 4000), Time=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left( 16.1178393915308, \\  12.3674609661102\\right)$"
      ],
      "text/plain": [
       "(16.117839391530826, 12.36746096611023)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VG2.PIDE_price((14000, 10000), Time=True)  # negative skewness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left( 18.1266742827993, \\  12.1112761497498\\right)$"
      ],
      "text/plain": [
       "(18.12667428279933, 12.111276149749756)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VG3.PIDE_price((14000, 10000), Time=True)  # positive skewness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1800x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(18, 6))\n",
    "ax1 = fig.add_subplot(121)\n",
    "ax2 = fig.add_subplot(122)\n",
    "\n",
    "ax1.plot(BS.S_vec, BS.price_vec, color=\"red\", label=\"BS curve\")\n",
    "ax1.plot(VG2.S_vec, VG2.price_vec, color=\"green\", label=\"VG curve\")\n",
    "ax1.plot(VG2.S_vec, VG2.payoff_f(VG2.S_vec), color=\"black\", label=\"Payoff\")\n",
    "ax1.set_xlim(50, 150)\n",
    "ax1.set_ylim(0, 50)\n",
    "ax1.set_xlabel(\"S\")\n",
    "ax1.set_ylabel(\"price\")\n",
    "ax1.set_title(\"VG vs BS - same variance - negative skewness\")\n",
    "ax1.legend()\n",
    "\n",
    "ax2.plot(BS.S_vec, BS.price_vec, color=\"red\", label=\"BS curve\")\n",
    "ax2.plot(VG3.S_vec, VG3.price_vec, color=\"green\", label=\"VG curve\")\n",
    "ax2.plot(VG3.S_vec, VG3.payoff_f(VG3.S_vec), color=\"black\", label=\"Payoff\")\n",
    "ax2.set_xlim(50, 170)\n",
    "ax2.set_ylim(0, 80)\n",
    "ax2.set_xlabel(\"S\")\n",
    "ax2.set_ylabel(\"price\")\n",
    "ax2.set_title(\"VG vs BS - same variance - positive skewness\")\n",
    "ax2.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1]  Madan, D., Carr, P., and Chang, E. (1998). \"The Variance Gamma process and option pricing\". European Finance Review, 2, 79--105."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
